• Homework• KCL/KVL Review• Bode Plots• Active Filters

Homework-due 3/6 (Najera), due 3/9 (Quinones)

P17 and P18

Questions?

SUCCESS POINTS:

• REPORT WRITING –

CHECK TO MAKE SURE

EVERYTHING YOU SAY

REFER DIRECTLY TO

YOUR TABLES AND

GRAPHS?

xxKVL/KCL Review

Use KCL and KVL to determine the values of the currents I1, I2 and I3.

THIS EXAMPLE SHOWS

HOW TO DEVELOP A

STRAGEDY TO SOLVE A

SYSTEM OF EQUATIONS.

I1

I2

I3

System of Equations: Adding Equations

BASED ON THESE

EQUATIONS, CURRENT HAS

UNITS OF AMPS (A)

System of Equations: Adding Equations

𝐴 103𝑚𝐴

1 𝐴=

I1 =5

1500I1 = 0.00333 𝐴

1500 𝐼1 = 5

System of Equations: Adding Equations

103𝑚𝐴

𝐴=

System of Equations: Adding Equations

•

I1=3.33 mA

I2=1.67 mA

I3=1.67 mA

xxKVL/KCL: In-Class Exercise

Use KCL and KVL to determine the values of the currents I1, I2 and I3.

THIS EXAMPLE SHOWS

HOW TO DEVELOP A

STRAGEDY TO SOLVE A

SYSTEM OF EQUATIONS.

I1

I2

I3

A

B

I1

I2

I3

xxKVL/KCL: In-Class Exercise

Use KCL and KVL to determine I1 through I4. Label all steps.

Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

xxKVL/KCL: In-Class Exercise

Using the KCL method, find I1 and I2.

Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

xxKVL/KCL: In-Class Exercise

Using the KCL method, find I1 – I3.

Source: Ulaby and Maharbiz, Circuits, Tech and Science Press, 2013.

When have circuits with AC signals, can analyze with

Bode Plot

(Magnitude vs Frequency)

Example: Filters

What is a Bode Plot?

A Bode Plot consists of:

Two plots used to interpret how the filter affects the input in terms of both magnitude and phase.

x Axis: Logarithm scale of frequency on x axis for both plots (f or )

y Axis Plot 1: Magnitude in units of decibels (dB)

y Axis Plot 2: Phase angle in degrees

Source: http://www.ece.utah.edu/~ee3110/bodeplot.pdf

ANGULAR FREQUENCY

SYMBOL:

UNITS: RADIANS/SECOND

FREQUENCY

SYMBOL: f

UNITS: CYCLES/SECOND

OR Hz

Bode Plots

Image Source: http://www.jensign.com/Discovery/bode/

LOW PASS FILTER HIGH PASS FILTER

ELIMINATES SIGNAL ABOVE fc

ELIMINATES SIGNAL BELOW fcY AXIS – dB - DECIBELS

Y AXIS – DEGREES

Bode Plots

Image Source: http://www.jensign.com/Discovery/bode/

LOW PASS FILTER HIGH PASS FILTER

RECALL THAT THE BODE PLOT:

• ILLUSTRATES THE GAIN IN THE SIGNAL (INPUT

VS OUTPUT), AND

• THE PHASE DIFFERENCE BETWEEN THE INPUT

AND OUTPUT SIGNALS

Bode Plots

WHAT IS THE DECREASE IN THE SIGNAL (OUTPUT VS INPUT)

IN UNITS OF

dB (DECIBEL) PER DECADE IN FREQUENCY?

EX. 1 DECADE WOULD BE BETWEEN 104 – 105 Hz

SO ON THE GRAPH, NEED TO DETERMINE HOW MUCH THE SIGNAL

DECREASES IN dB BETWEEN THESE FREQUENCY VALUES?

Bode Plots

Image Source: http://www.jensign.com/Discovery/bode/

LOW PASS FILTER HIGH PASS FILTER

20 dB PER DECADE

20 dB PER DECADE

xxOp-Amp Theory and Circuit Analysis An Op-Amp is an active device since it needs a power supply

to operate.

The Op-Amp has 2 inputs and 1 output.

How many pins are on the Op-Amp chip that we use?

- 3 pins per Op-Amp, 12 pins total, plus 2 pins for +Vss and –Vss, so 14 total pins

Image source: http://elektronikadasar.info/wp-content/uploads/2013/01/OP-Amp.png

SYMBOL(normally

don’t show +Vss and –

Vss)

xxLocation of the 4 Op-Amps on your LMC6484 chip.

Op-Amp Chip (LMC6484 Op-Amp)

xxNotice where the voltage connections are (V+ will be connected to 5V, and V- will be connected to ground). Therefore, orient the Op-Amp so you can connect easily to 5 V and ground.

Op-Amp Chip (LMC6484 Op-Amp)

xxNotice that for each Op-Amp, the outputs are all at the corners of the chip.

It does not matter which Op-Amp you use, as long as it is practical for your circuit design.

Op-Amp Chip (LMC6484 Op-Amp)

xxNotice where the inverting (-) and non-inverting (+) inputs are for each Op-Amp on the chip, and that the inverting (-) input is always next to the output pins.

Op-Amp Chip (LMC6484 Op-Amp)

+ -

+ -

+-

+-

xxOp-Amp Theory and Circuit Analysis Power Supply (Vcc – not shown)

The inputs (non-inverting (+) and inverting (-) to the op-amp draw no current (i.e. i = 0 into both inputs).

The two input voltages values are equal to each other (Vn = Vp). Ex. If Vref is ground, then Vn = Vp = 0 V.

One output, Vout.

OpAmp can saturate if Vout is greater than Vcc!!!! -more about this later

VinVout

Vref

Vn

Vp

R1

R2

i=0

i=0 +

-

xx

Types of Op-Amps we cover in this course:

Op-Amp Theory and Circuit Analysis

Voltage Follower or Buffer: Sets the voltage at that point in the circuit

Inverting Amplifier: Inverts the signal horizontally, and amplifies the signal

Non-Inverting Amplifier: Amplifies the signal

Filter OpAmp: Filters the signal: low, high or band pass

Can

an

alyz

e w

ith

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CL

/KV

L

Can

an

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ance

xxVoltage Follower or Buffer

Used to isolate two circuits

Input Voltage

Output VoltageVoltage = Input Voltage

Input Voltage

No Current

Key Review Question

What information do you need to determine the current flowing through a resistor?

The Resistor Value

The Voltage Drop Across the Resistor

xxInverting Amplifier

Vin Vout

Vref = Ground

Vp

VnR1

R2

𝑽𝒑 = 𝑽𝒏 = 𝑽𝒓𝒆𝒇 = 𝑮𝒓𝒅 = 𝟎

KCL: 𝑰𝟏 + 𝑰𝟐 = 𝟎(currents entering a node are zero)

or

𝑰𝟏 = −𝑰𝟐

𝑽𝒊𝒏 − 𝑽𝒏

𝑹𝟏=

−(𝑽𝒐𝒖𝒕−𝑽𝒏)

𝑹𝟐

𝑉𝑖𝑛

𝑅1=

−𝑉𝑜𝑢𝑡

𝑅2

𝑰𝟏

𝑰𝟐

𝑽𝒐𝒖𝒕

𝑽𝒊𝒏= −

𝑹𝟐

𝑹𝟏𝒘𝒉𝒆𝒓𝒆 𝒕𝒉𝒆 𝑮𝒂𝒊𝒏 = −

𝑹𝟐

𝑹𝟏

-

+KVL:

xxInverting Amplifier𝑽𝒐𝒖𝒕

𝑽𝒊𝒏= −

𝑹𝟐

𝑹𝟏𝒘𝒉𝒆𝒓𝒆 𝒕𝒉𝒆 𝑮𝒂𝒊𝒏 = −

𝑹𝟐

𝑹𝟏

WHAT IS THE APPROXIMATE RELATIONSHIP BETWEEN R1 AND R2?

xxCircuit Exercise IV - Non-Inverting Op-Amp

Assuming Vin = Vn and ip = in = O, use KCL to write an expression for Vout/Vin.

VoutVp

Vn

𝑰𝟐

𝑰𝟏

Vinip=0

in=0

R2 = 25 k

R1 = 10 k

xxLow Pass Filter

R1

R2

C1

Vref

Vout

Vin

Low Pass Filter

𝑮𝒂𝒊𝒏 = −𝑹𝟐

𝑹𝟏

Where the gain of the Op-Amp is equal to …

Homework-due 3/20 (Najera), due 3/23 (Quinones)

P19 and P20

Module V: Oxygen SensorOperational Amplifier

Build and analyze buffer, inverting amplifier, and photodiode oxygen sensor circuits.

SUCCESS POINTS:

• TRY EXPLAINING HOW

A BODE PLOT WORKS

TO A TEAM MEMBER,

AND THEN HAVE THEM

EXPLAIN IT TO YOU.

What’s Next in Week 10?

Will introduce…

LAB• Module V: Oxygen Sensor

LECTURE • Quiz 4

• KCL and KVL

• Active Component Op-Amp Theory

Please bring laptops to all lectures and labs.

Questions?